Solve for $x$ and $y$ using elimination. ${-6x-2y = -70}$ ${5x+2y = 61}$
We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-2y$ and $2y$ cancel out. $-x = -9$ $\dfrac{-x}{{-1}} = \dfrac{-9}{{-1}}$ ${x = 9}$ Now that you know ${x = 9}$ , plug it back into $\thinspace {-6x-2y = -70}\thinspace$ to find $y$ ${-6}{(9)}{ - 2y = -70}$ $-54-2y = -70$ $-54{+54} - 2y = -70{+54}$ $-2y = -16$ $\dfrac{-2y}{{-2}} = \dfrac{-16}{{-2}}$ ${y = 8}$ You can also plug ${x = 9}$ into $\thinspace {5x+2y = 61}\thinspace$ and get the same answer for $y$ : ${5}{(9)}{ + 2y = 61}$ ${y = 8}$